RALEIGH, N.C. — North Carolina has become a prime market for the smartphone-based car services Uber and Lyft — and is likely to join a push around the country to regulate the fast-growing businesses.

A big draw for the companies is the state’s mix of mid-sized cities, which are full of college students but lack extensive mass transit networks to serve their spread-out geography.

The companies’ expansion has legislators in North Carolina and elsewhere scrambling to study their business models ahead of sessions in 2015 when they could address insurance, car inspections or criminal background checks.

Transportation analyst Douglas Shinkle of the National Conference of State Legislatures thinks at least 20 legislatures are likely to take up legislation on Uber, Lyft and similar services in 2015 after several passed laws this year.